This paper attends to the problem of vibration of a self-excited mechanical system with a relatively complicated, history dependent dry friction model. The experimentally identified friction model allows description of various cases of stationary and transient motion. The system is composed of a lumped mass that interacts with a belt by means of dry friction. The system is additionally subjected to an external harmonic excitation through elastic element. The main objective of the experimental research has been focused on the analysis of the system behaviour for various values of the excitation frequency. This paper includes also computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis. The comparison enables the assumed friction model for steel-polyester pair to be verified. It was another goal of the investigations.